Abstract semantic graph¶
A graph representation of a formal expression or program whose nodes denote terms or semantic entities and whose shared nodes can represent common subexpressions beyond an abstract syntax tree.
Core Idea¶
ASGs or term graphs compact repeated structure, support common-subexpression elimination and graph rewriting, and may use directed acyclic structure for sharing or cycles for recursive definitions under explicit binding and mutation rules. Parsing and semantic analysis map occurrences to typed nodes, identical or equivalent subterms can share a node, directed edges encode argument or dependency roles, and graph rewrites transform the representation while preserving declared meaning. The abstraction is therefore identified by a declared carrier, a transformation or constraint over that carrier, and an invariant that tells an analyst whether the named structure is genuinely present.
Scope of Application¶
Abstract semantic graph belongs to compiler intermediate representations and is useful where the analyst can specify the typed compiler intermediate representations carrier, defining objects and relations, parameters, conventions, evidence, boundary cases, and comparison targets, then evaluate the source language, graph node and edge types, term and binding semantics, sharing criterion, acyclic or cyclic allowance, identity versus equality, typing, source-location mapping, mutation and rewrite rules, serialization, and semantic-preservation claim are explicit. The scope is broad within that domain but bounded by the need for the source language, graph node and edge types, term and binding semantics, sharing criterion, acyclic or cyclic allowance, identity versus equality, typing, source-location mapping, mutation and rewrite rules, serialization, and semantic-preservation claim are explicit.
Clarity¶
The abstraction clarifies a crowded vocabulary by making the source language, graph node and edge types, term and binding semantics, sharing criterion, acyclic or cyclic allowance, identity versus equality, typing, source-location mapping, mutation and rewrite rules, serialization, and semantic-preservation claim are explicit the center of the account. A claim should name the carrier, the governing operation or relation, the applicable assumptions, and the recognition test.
Manages Complexity¶
Without the abstraction, an analyst must reason directly over many local details: the carrier roles, admissibility assumptions, competing conventions, derived invariants, boundary cases, and proof or validation obligations specific to Abstract semantic graph. Abstract semantic graph compresses them into the roles in the structural signature. That compression permits comparison across instances without erasing the variables that determine validity. It also exposes which details may be varied safely and which are constitutive.
Abstract Reasoning¶
- Identify the carrier. State what the elements, states, objects, or observations are: the typed compiler intermediate representations carrier, defining objects and relations, parameters, conventions, evidence, boundary cases, and comparison targets. Reject examples whose alleged carrier belongs to a different problem. 2. Lock the constitutive rule. Express the source language, graph node and edge types, term and binding semantics, sharing criterion, acyclic or cyclic allowance, identity versus equality, typing, source-location mapping, mutation and rewrite rules, serialization, and semantic-preservation claim are explicit independently of one notation or implementation.
Knowledge Transfer¶
Knowledge transfers strongly among subfields of compiler intermediate representations because they reuse the typed compiler intermediate representations carrier, defining objects and relations, parameters, conventions, evidence, boundary cases, and comparison targets, Parsing and semantic analysis map occurrences to typed nodes, identical or equivalent subterms can share a node, directed edges encode argument or dependency roles, and graph rewrites transform the representation while preserving declared meaning., and type the carrier, state every parameter and convention in the definition, test that the source language, graph node and edge types, term and binding semantics, sharing criterion, acyclic or cyclic allowance, identity versus equality, typing, source-location mapping, mutation and rewrite rules, serialization, and semantic-preservation claim are explicit, compare the nearest accepted identity, and report counterexamples, uncertainty, and limiting cases.
Relationships to Other Abstractions¶
Current abstraction Abstract semantic graph Domain-specific
Parents (1) — more general patterns this builds on
-
Abstract semantic graph is a kind of Symbolic Representation Prime
The proposed strict upward parent is
prime:symbolic_representation.
Hierarchy path (1) — routes to 1 parentless root
- Abstract semantic graph → Symbolic Representation → Representation → Abstraction
Neighborhood in Abstraction Space¶
Abstract semantic graph sits in a crowded region of the domain-specific corpus (15th percentile for distinctiveness): several abstractions share nearly its structure, so a description that fits it tends to fit its neighbors too.
Family — Formal Grammars & Language Hierarchies (16 abstractions)
Nearest neighbors
- Semantic analysis (compilers) — 0.93
- Graph rewriting — 0.92
- Conceptual graph — 0.92
- Join (graph theory) — 0.92
- Orientation (graph theory) — 0.91
Computed from structural-signature embeddings · 2026-09-08